Abstract

The understanding of wildfires is increasingly important around the world with climate change causing drier conditions and leading to more intense fires. The purpose of this study is to explore the forward time center space method to solve partial differential equations that are incorporated into a reaction-diffusion system of wildfires. This system focuses on the change in fuel and temperature of the fire. Using the FTCS, we obtain an approximation to the solution of the wild- fire system of equations, allowing us to plot temperature and fuel at different time stamps using python. We break the wildfire reaction-diffusion to have a simple system without wind velocity and a full system that does involve wind velocity. In the simple system, we find that the diffusion rate and the set temperature rise per time step are the most influential in the change of fuel and temperature at each time step. A high diffusion rate lowers the temperature levels of the system. Therefore, a higher diffusion rate prolongs the existence of fuel. In the full system, including wind, we explore the ideas associated with the directional derivative. After investigating five different wind velocity vectors, we find that the addition of the wind pushes the temperature into a concentrated locations. Furthermore, wind dampens the overall temperature of the system with respect to the simple system. Overall, we create a basis for the study of wildfires to understand the intricate details of a reaction-diffusion system.

Advisor

Long, Colby

Department

Mathematics

Disciplines

Numerical Analysis and Computation | Other Mathematics | Partial Differential Equations

Keywords

Finite Difference Methods, Reaction-Diffusion, Wildfires, Partial Differential Equations

Publication Date

2021

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis

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